It is well established by X-ray crystal analysis that the mineral constituent of bone and of the enamel and dentine of teeth is essentially hydroxy-apatite Ca5OH(PO4)3, and that hydroxy-apatite has a structure differing only in small details from that of the well-crystallized mineral fluor-apatite Ca5F(PO4)3. The main difference, and in fact the only fully established one, between the two structures is that the hydroxy-apatite has a slightly larger unit cell than that of the fluor-apatite. The structure of the latter has been determined by Náray-Szabó, and by Mehmel who finally agrees with Náray-Szabó. We have made what is probably a more accurate determination of the structure, using more extensive X-ray data.